Estudo comparativo de métricas de ranking em Redes Sociais

The use of modeling and application of complex networks in several areas of knowledge have become an important tool for understanding different phenomena; among them some related to the structures and dissemination of information on social medias. In this sense, the use of a network's vertex ranking can be applied in the detection of influential nodes and possible foci of information diffusion. However, calculating the position of the vertices in some of these rankings may require a high computational cost. This paper presents a comparative study between six ranking metrics applied in different social medias. This comparison is made using the rank correlation coefficients. In addition, a study is presented on the computational time spent by each ranking. Results show that the Grau ranking metric has a greater correlation with other metrics and has low computational cost in its execution, making it an efficient indication in detecting influential nodes when there is a short term for the development of this activity.

Visual attention method based on vertex ranking of graphs by heterogeneous image attributes

The paper discusses a method of visual attention based on vertex ranking of graphs on the basis of image features. The aim of the research is to develop a method that allows high-precision detection of objects in images with low color contrast between the selected and background areas. The image is pre-segmented into regions to calculate the saliency map. The graph is based on regions. Each region is associated with related regions, as well as with areas adjacent to adjacent regions. The regions are vertices of the graph. The vertices of the graph are ranked according to the characteristics of the corresponding image areas. The scope is highlighted based on requests from background areas. The saliency map is determined based on background area queries. Regions adjacent to the edges of the image belong to the background areas. Color features of the image were used in the existing approach of visual attention based on the manifold ranking. Texture features and shape features are additionally used in the proposed method to improve accuracy. Gabor's energy function is used to calculate texture features. The distance between centers of the regions is calculated by analyzing the form. The proposed method has shown good results for detecting objects in images in which the background color and object color are in similar ranges. The experimental results are presented on test images. Precision-recall curves showing the advantage of the developed method are constructed.

On decay centrality in graphs

The decay centrality of a vertex $v$ in a graph $G$ with respect to a parameter $\delta \in (0,1)$ is a polynomial in δ such that for fixed $k$ the coefficient of $\delta ^k$ is equal to the number of vertices of $G$ at distance $k$ from $v$. This invariant (introduced independently by Jackson and Wolinsky in 1996 and Dangalchev in 2011) is considered as a replacement for the closeness centrality for graphs, however its unstability was pointed out by Yang and Zhuhadar in 2011. We explore mathematical properties of decay centrality depending on the choice of parameter δ and the stability of vertex ranking based on this centrality index.

CS_TOTR: A new vertex centrality method for directed signed networks based on status theory

Measuring the importance (or centrality) of vertices in a network is a significant topic in complex network analysis, which has significant applications in diverse domains, for example, disease control, spread of rumors, viral marketing and so on. Existing studies mainly focus on social networks with only positive (or friendship) relations, while signed networks with also negative (or enemy) relations are seldom studied. Various signed networks commonly exist in real world, e.g. a network indicating friendship/enmity, love/hate or trust/mistrust relationships. In this paper, we propose a new centrality method named CS_TOTR to give a ranking of vertices in directed signed networks. To design this new method, we use the “status theory” for signed networks, and also adopt the vertex ranking algorithm for a tournament and the topological sorting algorithm for a general directed graph. We apply this new centrality method on the famous Sampson Monastery dataset and obtain a convincing result which shows its validity.

On-line ranking of split graphs

Graphs and Algorithms International audience A vertex ranking of a graph G is an assignment of positive integers (colors) to the vertices of G such that each path connecting two vertices of the same color contains a vertex of a higher color. Our main goal is to find a vertex ranking using as few colors as possible. Considering on-line algorithms for vertex ranking of split graphs, we prove that the worst case ratio of the number of colors used by any on-line ranking algorithm and the number of colors used in an optimal off-line solution may be arbitrarily large. This negative result motivates us to investigate semi on-line algorithms, where a split graph is presented on-line but its clique number is given in advance. We prove that there does not exist a (2-ɛ)-competitive semi on-line algorithm of this type. Finally, a 2-competitive semi on-line algorithm is given.